<p>Groundwater recharge remains a notoriously difficult flux to estimate, despite ongoing scientific&#160;efforts. In recent years, time series modeling using impulse response functions has gained&#160;popularity to simulate groundwater levels and is quickly becoming a common tool for&#160;hydrogeologists. Several approaches have been developed to estimate recharge from time series&#160;models for both linear and non-linear systems (e.g., [1], [2], and [3]). In this study, we introduce a&#160;novel approach to estimate groundwater recharge from observed groundwater levels in nonlinear&#160;systems (i.e., twice the precipitation does not necessarily lead to twice the recharge). We&#160;extend a time series model using impulse response functions with a non-linear unsaturated zone&#160;module that simulates recharge. The model parameters are estimated by fitting the simulated to&#160;the observed groundwater levels, with the groundwater recharge as an intermediate model result.&#160;</p><p>The method is tested on a time series of groundwater levels observed in Southeastern Austria&#160;(Wagna), where lysimeter data of seepage to the groundwater is available for model validation.&#160;The simulated groundwater recharge suggests an event-based recharge behavior, with most&#160;recharge occurring shortly after larger precipitation events. This finding agrees with the behavior&#160;observed in the lysimeter data. The estimated recharge fluxes show a high correlation with the&#160;observed seepage on time scales from years to months or weeks, while daily recharge rates show&#160;larger errors. Advantages of the method include limited data requirements (only precipitation,&#160;potential evapotranspiration, and groundwater time series are required) and the possibility to&#160;correct for other factors causing groundwater level fluctuations (e.g., pumping, river levels). This&#160;makes it possible to apply the method in locations where little system knowledge (e.g., soil&#160;profiles) is available.</p><p><strong>References:</strong><br>[1] Besbes, M. and De Marsily, G. (1984) From infiltration to recharge: use of a parametric transfer&#160;function, Journal of Hydrology.<br>[2] Peterson, T.J. and Fulton, S. (2019) Joint estimation of gross recharge, groundwater usage, and&#160;hydraulic properties within HydroSight, Groundwater.<br>[3] Obergfell, C., Bakker, M. and Maas, K. (2019) Estimation of average diffuse aquifer recharge&#160;using time series modeling of groundwater heads, Groundwater.</p>
Unwrapping the phase response functions for non-linear systems